Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 97.9% → 97.9%

Time: 2.2s

Alternatives: 9

Speedup: 1.0×

• 34.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 91.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{z \cdot t}{16}\\ t_2 := t\_1 - \frac{a \cdot b}{4}\\ \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 3.6 \cdot 10^{+39}:\\ \;\;\;\;t\_1 + c\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* z t) 16.0))) (t_2 (- t_1 (/ (* a b) 4.0))))
   (if (<= (* a b) -6e+59) t_2 (if (<= (* a b) 3.6e+39) (+ t_1 c) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((z * t) / 16.0);
	double t_2 = t_1 - ((a * b) / 4.0);
	double tmp;
	if ((a * b) <= -6e+59) {
		tmp = t_2;
	} else if ((a * b) <= 3.6e+39) {
		tmp = t_1 + c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + ((z * t) / 16.0d0)
    t_2 = t_1 - ((a * b) / 4.0d0)
    if ((a * b) <= (-6d+59)) then
        tmp = t_2
    else if ((a * b) <= 3.6d+39) then
        tmp = t_1 + c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((z * t) / 16.0);
	double t_2 = t_1 - ((a * b) / 4.0);
	double tmp;
	if ((a * b) <= -6e+59) {
		tmp = t_2;
	} else if ((a * b) <= 3.6e+39) {
		tmp = t_1 + c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((z * t) / 16.0)
	t_2 = t_1 - ((a * b) / 4.0)
	tmp = 0
	if (a * b) <= -6e+59:
		tmp = t_2
	elif (a * b) <= 3.6e+39:
		tmp = t_1 + c
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	t_2 = Float64(t_1 - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (Float64(a * b) <= -6e+59)
		tmp = t_2;
	elseif (Float64(a * b) <= 3.6e+39)
		tmp = Float64(t_1 + c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((z * t) / 16.0);
	t_2 = t_1 - ((a * b) / 4.0);
	tmp = 0.0;
	if ((a * b) <= -6e+59)
		tmp = t_2;
	elseif ((a * b) <= 3.6e+39)
		tmp = t_1 + c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -6e+59], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 3.6e+39], N[(t$95$1 + c), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -6.0000000000000001e59 or 3.59999999999999984e39 < (*.f64 a b)

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

   5. Applied rewrites 94.0%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

   if -6.0000000000000001e59 < (*.f64 a b) < 3.59999999999999984e39

   1. Initial program 98.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]

   5. Applied rewrites 97.1%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right)} + c \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 68.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \frac{a \cdot b}{4}\\ \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 3.9 \cdot 10^{-51}:\\ \;\;\;\;x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{elif}\;a \cdot b \leq 3.6 \cdot 10^{+39}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (/ (* a b) 4.0))))
   (if (<= (* a b) -9.5e+124)
     t_1
     (if (<= (* a b) 3.9e-51)
       (+ (* x y) (/ (* z t) 16.0))
       (if (<= (* a b) 3.6e+39) (+ (* x y) c) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) / 4.0);
	double tmp;
	if ((a * b) <= -9.5e+124) {
		tmp = t_1;
	} else if ((a * b) <= 3.9e-51) {
		tmp = (x * y) + ((z * t) / 16.0);
	} else if ((a * b) <= 3.6e+39) {
		tmp = (x * y) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((a * b) / 4.0d0)
    if ((a * b) <= (-9.5d+124)) then
        tmp = t_1
    else if ((a * b) <= 3.9d-51) then
        tmp = (x * y) + ((z * t) / 16.0d0)
    else if ((a * b) <= 3.6d+39) then
        tmp = (x * y) + c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) / 4.0);
	double tmp;
	if ((a * b) <= -9.5e+124) {
		tmp = t_1;
	} else if ((a * b) <= 3.9e-51) {
		tmp = (x * y) + ((z * t) / 16.0);
	} else if ((a * b) <= 3.6e+39) {
		tmp = (x * y) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) / 4.0)
	tmp = 0
	if (a * b) <= -9.5e+124:
		tmp = t_1
	elif (a * b) <= 3.9e-51:
		tmp = (x * y) + ((z * t) / 16.0)
	elif (a * b) <= 3.6e+39:
		tmp = (x * y) + c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (Float64(a * b) <= -9.5e+124)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.9e-51)
		tmp = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0));
	elseif (Float64(a * b) <= 3.6e+39)
		tmp = Float64(Float64(x * y) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((a * b) / 4.0);
	tmp = 0.0;
	if ((a * b) <= -9.5e+124)
		tmp = t_1;
	elseif ((a * b) <= 3.9e-51)
		tmp = (x * y) + ((z * t) / 16.0);
	elseif ((a * b) <= 3.6e+39)
		tmp = (x * y) + c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -9.5e+124], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.9e-51], N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.6e+39], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.50000000000000004e124 or 3.59999999999999984e39 < (*.f64 a b)

   1. Initial program 99.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

   5. Applied rewrites 93.3%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) - \frac{\color{blue}{a \cdot b}}{4} \]

   8. Applied rewrites 83.7%

      \[\leadsto x \cdot y - \frac{\color{blue}{a \cdot b}}{4} \]

   if -9.50000000000000004e124 < (*.f64 a b) < 3.8999999999999997e-51

   1. Initial program 98.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

   5. Applied rewrites 74.8%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) - \color{blue}{\frac{1}{4} \cdot \left(a \cdot b\right)} \]

   8. Applied rewrites 70.6%

      \[\leadsto x \cdot y + \color{blue}{\frac{z \cdot t}{16}} \]

   if 3.8999999999999997e-51 < (*.f64 a b) < 3.59999999999999984e39

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]

   5. Applied rewrites 92.5%

      \[\leadsto \color{blue}{x \cdot y} + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + c\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;a \cdot b \leq -9.8 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 80:\\ \;\;\;\;\left(x \cdot y + \frac{z \cdot t}{16}\right) + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) c) (/ (* a b) 4.0))))
   (if (<= (* a b) -9.8e+124)
     t_1
     (if (<= (* a b) 80.0) (+ (+ (* x y) (/ (* z t) 16.0)) c) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + c) - ((a * b) / 4.0);
	double tmp;
	if ((a * b) <= -9.8e+124) {
		tmp = t_1;
	} else if ((a * b) <= 80.0) {
		tmp = ((x * y) + ((z * t) / 16.0)) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) + c) - ((a * b) / 4.0d0)
    if ((a * b) <= (-9.8d+124)) then
        tmp = t_1
    else if ((a * b) <= 80.0d0) then
        tmp = ((x * y) + ((z * t) / 16.0d0)) + c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + c) - ((a * b) / 4.0);
	double tmp;
	if ((a * b) <= -9.8e+124) {
		tmp = t_1;
	} else if ((a * b) <= 80.0) {
		tmp = ((x * y) + ((z * t) / 16.0)) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + c) - ((a * b) / 4.0)
	tmp = 0
	if (a * b) <= -9.8e+124:
		tmp = t_1
	elif (a * b) <= 80.0:
		tmp = ((x * y) + ((z * t) / 16.0)) + c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + c) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (Float64(a * b) <= -9.8e+124)
		tmp = t_1;
	elseif (Float64(a * b) <= 80.0)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + c) - ((a * b) / 4.0);
	tmp = 0.0;
	if ((a * b) <= -9.8e+124)
		tmp = t_1;
	elseif ((a * b) <= 80.0)
		tmp = ((x * y) + ((z * t) / 16.0)) + c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -9.8e+124], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 80.0], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.80000000000000069e124 or 80 < (*.f64 a b)

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

   5. Applied rewrites 91.0%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) - \frac{\color{blue}{a \cdot b}}{4} \]

   8. Applied rewrites 89.3%

      \[\leadsto \left(x \cdot y + c\right) - \frac{\color{blue}{a \cdot b}}{4} \]

   if -9.80000000000000069e124 < (*.f64 a b) < 80

   1. Initial program 98.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]

   5. Applied rewrites 94.6%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right)} + c \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 86.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;z \cdot t \leq -1.65 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 4.5 \cdot 10^{+89}:\\ \;\;\;\;\left(x \cdot y + c\right) - \frac{a \cdot b}{4}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* z t) 16.0))))
   (if (<= (* z t) -1.65e+143)
     t_1
     (if (<= (* z t) 4.5e+89) (- (+ (* x y) c) (/ (* a b) 4.0)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -1.65e+143) {
		tmp = t_1;
	} else if ((z * t) <= 4.5e+89) {
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + ((z * t) / 16.0d0)
    if ((z * t) <= (-1.65d+143)) then
        tmp = t_1
    else if ((z * t) <= 4.5d+89) then
        tmp = ((x * y) + c) - ((a * b) / 4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -1.65e+143) {
		tmp = t_1;
	} else if ((z * t) <= 4.5e+89) {
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((z * t) / 16.0)
	tmp = 0
	if (z * t) <= -1.65e+143:
		tmp = t_1
	elif (z * t) <= 4.5e+89:
		tmp = ((x * y) + c) - ((a * b) / 4.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (Float64(z * t) <= -1.65e+143)
		tmp = t_1;
	elseif (Float64(z * t) <= 4.5e+89)
		tmp = Float64(Float64(Float64(x * y) + c) - Float64(Float64(a * b) / 4.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((z * t) / 16.0);
	tmp = 0.0;
	if ((z * t) <= -1.65e+143)
		tmp = t_1;
	elseif ((z * t) <= 4.5e+89)
		tmp = ((x * y) + c) - ((a * b) / 4.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1.65e+143], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 4.5e+89], N[(N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.65e143 or 4.5e89 < (*.f64 z t)

   1. Initial program 96.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

   5. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) - \color{blue}{\frac{1}{4} \cdot \left(a \cdot b\right)} \]

   8. Applied rewrites 78.3%

      \[\leadsto x \cdot y + \color{blue}{\frac{z \cdot t}{16}} \]

   if -1.65e143 < (*.f64 z t) < 4.5e89

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

   5. Applied rewrites 76.9%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) - \frac{\color{blue}{a \cdot b}}{4} \]

   8. Applied rewrites 92.6%

      \[\leadsto \left(x \cdot y + c\right) - \frac{\color{blue}{a \cdot b}}{4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;z \cdot t \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 5.1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot y + c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (/ (* z t) 16.0))))
   (if (<= (* z t) -1.25e+76)
     t_1
     (if (<= (* z t) 5.1e+15) (+ (* x y) c) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -1.25e+76) {
		tmp = t_1;
	} else if ((z * t) <= 5.1e+15) {
		tmp = (x * y) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + ((z * t) / 16.0d0)
    if ((z * t) <= (-1.25d+76)) then
        tmp = t_1
    else if ((z * t) <= 5.1d+15) then
        tmp = (x * y) + c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if ((z * t) <= -1.25e+76) {
		tmp = t_1;
	} else if ((z * t) <= 5.1e+15) {
		tmp = (x * y) + c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((z * t) / 16.0)
	tmp = 0
	if (z * t) <= -1.25e+76:
		tmp = t_1
	elif (z * t) <= 5.1e+15:
		tmp = (x * y) + c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (Float64(z * t) <= -1.25e+76)
		tmp = t_1;
	elseif (Float64(z * t) <= 5.1e+15)
		tmp = Float64(Float64(x * y) + c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((z * t) / 16.0);
	tmp = 0.0;
	if ((z * t) <= -1.25e+76)
		tmp = t_1;
	elseif ((z * t) <= 5.1e+15)
		tmp = (x * y) + c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1.25e+76], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 5.1e+15], N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.24999999999999998e76 or 5.1e15 < (*.f64 z t)

   1. Initial program 97.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

   5. Applied rewrites 87.8%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) - \color{blue}{\frac{1}{4} \cdot \left(a \cdot b\right)} \]

   8. Applied rewrites 72.0%

      \[\leadsto x \cdot y + \color{blue}{\frac{z \cdot t}{16}} \]

   if -1.24999999999999998e76 < (*.f64 z t) < 5.1e15

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]

   5. Applied rewrites 62.1%

      \[\leadsto \color{blue}{x \cdot y} + c \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 41.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4800000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.8 \cdot 10^{+81}:\\ \;\;\;\;a \cdot b + c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -4800000000000.0)
   (* x y)
   (if (<= (* x y) 2.8e+81) (+ (* a b) c) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -4800000000000.0) {
		tmp = x * y;
	} else if ((x * y) <= 2.8e+81) {
		tmp = (a * b) + c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-4800000000000.0d0)) then
        tmp = x * y
    else if ((x * y) <= 2.8d+81) then
        tmp = (a * b) + c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -4800000000000.0) {
		tmp = x * y;
	} else if ((x * y) <= 2.8e+81) {
		tmp = (a * b) + c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -4800000000000.0:
		tmp = x * y
	elif (x * y) <= 2.8e+81:
		tmp = (a * b) + c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -4800000000000.0)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.8e+81)
		tmp = Float64(Float64(a * b) + c);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -4800000000000.0)
		tmp = x * y;
	elseif ((x * y) <= 2.8e+81)
		tmp = (a * b) + c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -4800000000000.0], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.8e+81], N[(N[(a * b), $MachinePrecision] + c), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.8e12 or 2.79999999999999995e81 < (*.f64 x y)

   1. Initial program 98.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

   5. Applied rewrites 91.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) - \color{blue}{\frac{1}{4} \cdot \left(a \cdot b\right)} \]

   8. Applied rewrites 64.2%

      \[\leadsto x \cdot \color{blue}{y} \]

   if -4.8e12 < (*.f64 x y) < 2.79999999999999995e81

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]

   5. Applied rewrites 68.8%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right)} + c \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{1}{16} \cdot \color{blue}{\left(t \cdot z\right)} + c \]

   8. Applied rewrites 10.2%

      \[\leadsto \left(x \cdot y + \color{blue}{c}\right) + c \]

   9. Taylor expanded in x around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(-1 \cdot y + \frac{-1}{16} \cdot \frac{t \cdot z}{x}\right)\right)} + c \]

   11. Applied rewrites 27.5%

       \[\leadsto a \cdot \color{blue}{b} + c \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 48.5% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ x \cdot y + c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (+ (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (x * y) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (x * y) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (x * y) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (x * y) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(x * y) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (x * y) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]

5. Applied rewrites 48.6%

   \[\leadsto \color{blue}{x \cdot y} + c \]
6. Add Preprocessing

Alternative 9: 28.4% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ x \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (* x y))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x * y;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = x * y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x * y;
}

Python

def code(x, y, z, t, a, b, c):
	return x * y

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x * y)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x * y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x * y), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]

5. Applied rewrites 80.6%

   \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}} \]

6. Taylor expanded in x around 0

   \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) - \color{blue}{\frac{1}{4} \cdot \left(a \cdot b\right)} \]

8. Applied rewrites 31.1%

   \[\leadsto x \cdot \color{blue}{y} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))